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It looks like the timeout box is not being rendered for some reason. We'll be releasing an update this week for ProGet which will include a fix for that. For now, it is possible to set the timeout either directly in the database or using the API. If you have access to the SQL instance, probably the easiest thing to do is change the Timeout_Period value for the connector (it's in seconds). You can get the connector ID by looking at the URL for an edit connector link. After setting it, you'll probably need to restart the web site by going to the All Settings page and just clicking Save.
Sorry about this- we haven't needed to change the timeout period for a while.
As far as the poor performance goes, I imagine nuget.org simply is not optimizing anymore for the types of queries that our connector filters are using. If there's nothing simple they can do on their end, we'll figure something out, but hopefully it's just a temporary issue with them.